Categorical Propositions Exam 3 Flashcards
Relate Subject terms to predicate terms
(Connecting who or what the sentence is about to what they are doing)
Categorical Proposition
represents a person, thing, or concept (What or who the sentence is about)
Subject Term
What is said about the subject of the sentence
Predicate term
All S are P
No S are P
Some S are P
Some S are not P
Four types of categorical propositions
Word like “All” or “Some” are…
quantifier
Links the subject and predicate terms
copula
Always has a subject term that is a noun or noun phrase, a predicate term that is a noun or phrase, with a quantifier (All, no, or some), and a copula linking the subject and predicate terms (Are or are not)
standard form
Affirmative quality (“All” or “Some”) or Negative quality (“No” or “Some”) affirms or denies class membership of a categorical proposition
quality (categorical propositions)
Universal quality (“All” or “No”) or Particular quality (“Some”) of a categorical proposition
quantity (categorical proposition)
The statement applies to every member of the group it talks about (Applies to terms, not to propositions)
Distribution (categorical proposition)
A : Universal affirmative (S distributed)
E : Universal negative (S and P distributed)
I : Particular affirmative (S and P undistributed)
O: Particular negative(P distributed)
Letter names of the four categorical propositions
Statements or claims that can be either true or false
Propositions
Two perspectives : Aristotelean and Boolean.
Existential import
Using universal statements “All” or “No” implies that the subject of the statement exists
Aristotelian standpoint
developed by John Venn to represent the information expressed by categorical propositions
Venn Diagram
Something is true because there is nothing there that makes it is false.
Vacuously True
Something is wrong because there is nothing to make it true
Vacuously False
drawing a conclusion from one proposition without a lot of steps or complex reasoning. (“All cats have tails” conclusion “Some cats have tails”)
Immediate Inference
Saying something about an entire group as if it is real but no one knows if it is real or not.
Existential fallcy
When the subject and predicate switch places
Conversion
When the quality (Affirmative or negative) is changed and the predicate term is replace with its complement it is…
Observsion
When the subject and predicate switch places and replace each with its term compliment. (All horses are animals; all non-animals are non-horses)
Contraposition
When the subject and predicate switch places (No cats are dogs; No dogs are cats)
Converse statement
when the converse of an A,E,I, or O statement is mistakenly assumed to be true when it has invalid logic.
Fallacy of illicit conversion
everything that doesn’t belong to a specific set within a larger set of things. It includes all the elements that are not in that set.
Class complement
the exact opposite of the term (All cats are mammals; All cats are non-mammals)
Term complement
If a then b -> If not b then not A
The contrapositive of a given statement
When someone incorrectly switches the subject and the predicate of a statement in a contraposition leading to an invalid argument.
Fallacy of Illicit contraposition
Illustrates the relationship of mutually contradictory pairs of categorical propositions. If one is true the other is automatically false. (If all Cats are Black, Then none of the Cats are not Black)
Modern square of opposition
opposite truth value (A-0 and E-I)
contradictory relation
At least one of the propositions is false (A-E) one of them is false
contrary relation
At least one of the propositions is true (I-O) one of them must be true
subcontrary relation
The truth trickles down from A-I and E-O
The falsity trickles up from I-A and O-E
subalternation relation
illicit contrary
illicit subcontrary
illicit subalternation
conditionally valid
Statements that incorporate forms of the verb “to be” other than “are” and “are not: or omit it entirely need to have the implicit “are” or “are not” made explicit.
Ex: Some dogs would rather bark than bite
Some dogs ARE ANIMALS THAT would rather bark than bite
Nonstandard verbs
Propositions that make assertions about singular nouns can be transformed into universals by means of a “parameter”
singular propositions
A phrase that affects the number of the subject term without changing its meaning.
Ex: Socrates is mortal
ALL PEOPLE IDENTICAL TO Socrates are PEOPLE WHO ARE mortal
parameter
Implicit quantifies must be made explicit. to determine the quantity you must be sensitive to the most probable meaning of the statement.
unexpressed quantifiers
nonstandard quantifiers
conditional statements
Propositions using the words “Only” “None but” “None except etc.
exclusive propositions
exceptive propositions
What does A distribute?
The Subject
What does E distribute?
The Subject and the Predicate
What does I distribute?
Neither the subject nor the predicate
What does O distribute?
The Predicate
What does Universal quantity distribute?
Subjects
What do Negative quantity distribute?
Predicates
Arguments that are from the boolean standpoint are valid regardless of whether they refer to existing things.
Unconditionally Valid
When you change the quality (affirmative or negative) and replace the predicate with its term compliment (All horses are animals; no horses are non-animals)
Obversion
A false A proposition is equal to an…
O proposition
A false O proposition is equal to an…
A proposition
A false E proposition is equal to an…
I proposition
A false I proposition is equal to an…
E proposition
adverbs “Where” “Anywhere” “nowhere”) may be translated using the word “places”
Ex” Wherever you hide, they will find you and they will tax you”
Spatial adverbs
adverbs “When” “Whenever” “Always” may be translated using “times”
Ex: He is never clean shaven
Temporal adverbs
Pronouns (“Who” “Whoever” “Anyone”) may be translated using “people”
Personal Pronouns
Pronouns (“What” “Whatever” “Anything”) may be translated using “Things”
Impersonal Pronouns
